Question: John opened up a new bag of jelly beans and ate three-fourths of the jelly beans in the bag. Then Mike ate two-thirds of the remaining jelly beans. Finally, Fred ate the ten jelly beans that were left. How many jelly beans were in the unopened bag of jelly beans?
Explanation: Working backwards, we first consider how many jelly beans were in the bag when Fred got it. Since Fred ate the remaining $10$ jelly beans, there must have been $10$ jelly beans in the bag. Next, we know that after Mike ate $2/3$ of the jelly beans, there were $10$ left. Thus, when Mike got the bag, there must have been $30$ jelly beans in it. Finally, we know that John ate $3/4$ of the bag of jelly beans, leaving $30$ left. Since $30$ must be $1/4$ of the total number of jelly beans there were in the bag to begin with, the unopened bag contained $\boxed{120}$ jelly beans.